In order to clarify the fracture behavior of a unidirectional CFRP under proportional loading along the fiber (0°) and fiber vertical (90°) directions, a biaxial tensile test was carried out using a cruciform specimen with two symmetric flat indentations in the thickness direction. Three fracture modes were observed in the specimens after the test. The first mode was a transverse crack (TC), and the second was fiber breakage (FB). The third mode was a mixture mode of TC and FB (TC&FB). According to the measured fracture strains, regardless of the magnitude of the normal strain in the 0° direction, TC and TC&FB modes occurred when the normal strain in the 90° direction, εy, ranged from 0.08% to 1.26% (positive values), and the FB mode occurred when εy ranged from −0.19% to −0.79% (negative values). The TC&FB mode is a unique mode that does not appear as a failure mode under uniaxial tension; it only occurs under biaxial tensile loading. Biaxial tensile tests were also conducted under non-proportional loading. The result showed three fracture modes similarly to the proportional loading case, each of which was also determined by the positive or negative value of εy. Thus, this study reveals that the occurrence of each fracture mode in a unidirectional CFRP is characterized by only one parameter, namely εy.